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Copyright © 2019 by Morgan & Claypool
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in
any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations
in printed reviews, without the prior permission of the publisher.
Analytical Techniques for Solving Nonlinear Partial Differential Equations
Daniel J. Arrigo
www.morganclaypool.com
ISBN: 9781681735337 paperback
ISBN: 9781681735344 ebook
ISBN: 9781681735351 hardcover
DOI 10.2200/S00907ED1V01Y201903MAS025
A Publication in the Morgan & Claypool Publishers series
SYNTHESIS LECTURES ON MATHEMATICS AND STATISTICS
Lecture #25
Series Editor: Steven G. Krantz, Washington University, St. Louis
Series ISSN
Print 1938-1743 Electronic 1938-1751
Analytical Techniques for
Solving Nonlinear Partial
Differential Equations
Daniel J. Arrigo
University of Central Arkansas
SYNTHESIS LECTURES ON MATHEMATICS AND STATISTICS #25
C
M
&
cLaypoolMorgan publishers
&
ABSTRACT
is is an introduction to methods for solving nonlinear partial differential equations
(NLPDEs). After the introduction of several PDEs drawn from science and engineering, the
reader is introduced to techniques used to obtain exact solutions of NPDEs. e chapters include
the following topics: Compatibility, Differential Substitutions, Point and Contact Transforma-
tions, First Integrals, and Functional Separability. e reader is guided through these chapters
and is provided with several detailed examples. Each chapter ends with a series of exercises
illustrating the material presented in each chapter.
e book can be used as a textbook for a second course in PDEs (typically found in both
science and engineering programs) and has been used at the University of Central Arkansas for
more than ten years.
KEYWORDS
nonlinear partial differential equations, compatibility, differential substitutions,
point and contact transformations, first integrals, functional separability
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